In Exercises 45–66, divide and, if possible, simplify.
____
√50xy...

Question

In Exercises 45–66, divide and, if possible, simplify.
____
√50xy
2√2

Accepted Answer

Welcome back. I am so glad you're here. We're asked for the following expression, perform division and further simplify if possible. The expression we're given is in the numerator, we have the square root of 300 H K that's divided by, in the denominator three square root three. Our answer choices are answer choice. A three square H K divided by 10 Answty Choice B square R H K divided by three answer trace C Square 10 HK All divided by three and Answice Choice D Square it three HK All divided by three. All right. Well, we notice that both the numerator and the denominator have a square rut, but the denominator also has this three outside of the square root. We have been going over in previous lessons when you are taking the root of both the numerator and the denominator. You can rewrite that by taking the root of the whole fraction. But this time, there's something that's not in the radical. So how do we deal with that? Well, we can factor that out in front so we can factor out this three, but it's in the denominator. So it's actually a one third, we can factor out a one third In front of our radical. And now we have the square root of both our numerator and our denominator inside the square root. And the numerator is 300 HK and inside the square root and the denominator is just the three. So now we can work to simplify what's inside of the radical. We can start off by taking 300 divided by 3, 300, divided by three is 100. So not forgetting our one third in front of the radical multiplied by now, it's the square root of not 300 H K divided by three, but it's now 100 H K And we can take the square root of 100, the square root of 100 is 10 because 100 is 10 squared. So we can rewrite this can't forget our one third in the front being multiplied by now, a 10 comes out of the radical but the H and the K remain inside of the radical. There are not, we can't take the square root of those, not enough factors of H S in cases. So now we can take the multiplication of the one third and the 10, 1 3rd multiplied by 10 is 13th. So we can rewrite this as 10 square rut H K all divided by three. And that's as simplified as this one gets, we look at our answer traces and this matches with answer trace. B well done. We'll catch you on the next one.

In Exercises 45–66, divide and, if possible, simplify. ____ √50xy 2√2

Key Concepts

Radical Expressions

Simplifying Radicals

Dividing Radicals

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